This paper considers the design and analysis of a pointwise optimal adaptive internal model control scheme. Using a series-parallel identification model, the "internal model" for an open loop stable plant is adapted on-line and the time-varying internal model control "parameter" is chosen in a certainty equivalence fashion to pointwise minimize an H-2 performance index. Stability of the resulting scheme and its robustness to plant modelling errors are established. The results here provide a suitable theoretical basis for analytically justifying some of the reported industrial successes of adaptive internal model control schemes.